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When smartphone cameras are used to take photos of digital screens, usually moire patterns result, severely degrading photo quality. In this paper, we design a wavelet-based dual-branch network (WDNet) with a spatial attention mechanism for image demoireing. Existing image restoration methods working in the RGB domain have difficulty in distinguishing moire patterns from true scene texture. Unlike these methods, our network removes moire patterns in the wavelet domain to separate the frequencies of moire patterns from the image content. The network combines dense convolution modules and dilated convolution modules supporting large receptive fields. Extensive experiments demonstrate the effectiveness of our method, and we further show that WDNet generalizes to removing moire artifacts on non-screen images. Although designed for image demoireing, WDNet has been applied to two other low-levelvision tasks, outperforming state-of-the-art image deraining and derain-drop methods on the Rain100h and Raindrop800 data sets, respectively.